Folia Microbiol. 31, 56-- 68 (1986)

Mathematical Modelling of the Digestion Process: Application Mass-Energy Balance* * *

I . H A V L i K , J . VOTRUBA a n d M. SOBOTKA

Department of Technical Microbiology, Institute of Microbiology, Czechoslovak Academy of Sciences, lg2 20 Prague 4

Anaerobic of Dynamic

Received December 21, 1985

ABSTRACT. The method of mass and energy balance was used in the design of a dynamic model of anaerobic digestion of complex organic substrates with production of methane. Distr ibution of mass flow, represented by the mos t abundan t elements (C, H, :N, O), and energy flow, re- presented by redoxons (available electrons), into gas and liquid ou tpu t s t reams is influenced by environmenta l conditions in a cont inuous flow digester. Two pa thways of methane generat ios , v/a cleavage of acetate and via carbon dioxide reduction by hydrogen, are described in the mode]. The model was compared with exper imental da ta from laboratory and pilot.plant exper iments

Nomenclature

Note:' Yields of acetate, CO2, 112, soluble organics and solid residue from hydrolytic and/or aeidogenic biomass (X) are denoted with Y i X , i ~ AC, CO2, 112, SO, $2. Yields of me thane and carbon dioxide from methanogenic biomass are denoted with YC1[4XM (methane formed by cleavage of acetate), YCH4X1[ (methane formed by COz reduction by 1[~) and YCO2XM. Values of these yields were obtained from mass - - ene rgy balance on the basis of the general formula Y i X = Yij[ Y X j , where Yi j is the stoichiomctric coefficient of conversion of substance j to substance i (i.e. yield o f i from j), and Y X j is the yield coefficient of biomass from substance j . Values of yield coefficients YN1[4X and YZX were not computed from mass - -ene rgy balance and were taken from Hill and Bar th (1977) (see Table I).

c concentrat ion

D dilution rate 2' gas flow rate

reel m - s kg nl-8 d-1 m 3 d - t L d -1 d-1 kLa gas transfer coefficient

K ionization constants (•I-14 +, 1[C03-) KAc sa tura t ion constant for growth on

unionized acetic acid KD death rate coefficient of hydrolytic

and/or aeidogenic bacteria (l -1 /~DM death rate coefficient of methanogenie bacteria d -1 K ~ 1[enry's law constants (H2, COs, NHa) reel k P a - l L -1

kg m -a

* Par t I I of the series Bioengineering Aspects of Anaerobic Digestion; par t I: Folia Microbiol. 2g, 196 (1983). ** Par t of this paper was presented at the International CHISA 8$ Conference held in Praline, September 3-- 7, 1984.

1986. ANAEROBIC DIGESTION PROCESS 57

g l ~ 2 Ki

KiAc

/~iN~3

Ks

~h M P PT r SV V V, X

XM

YACS 1 YACX

YCH4AC YCH4H2 YCH4S 1 YOiCUXM

YCH4XH

YCO2S1 YCO 2T u YCO2XM

YH2S1 ~ ' YH2X

L . '

YNH4X Yr~/s YTp/s

YSO~I. YSOX �9

YS2SI YS2X :-

YXMH2 YXSM YXS YXSO

YZX" "*

?

O

saturation constant for growth on H2 inhibition coefficient for unionized acetic acid in the growth

function of hydrolytic and/or acidogenic bacteria inhibition coefficient for unionized acetic acid in the growth

function of methanogenic bacteria inhibition coefficient for NH3 in the growth function

of methanogenic bacteria saturation constant in the growth function of hydrolytic

and/or acidogenic bacteria mass flow molar mass partial pressure total pressure reaction rate, transfer rate standard volume liquid phase volume gas phase volume biomass concentration of hydrolytic

and/or acidogenic bacteria biomass concentration of methanogenic bacteria

yield of acetate form primary substrato yield of acetate from hydrolytic and/or

acidogenic biomass yield of methane from acetate yield of methane from hydrogen yield of methane from primary suhstrate yield of methane from methanogenic biomass

(methane formed from acetate) yield of methane from methanogenic bioma'ss

(methane formed from hydrogen) yield of CO2 formed directly from primary substrate yield of total CO2 from primary substrate yield of CO2 from hydrolytic and/or acidogenic biomass

yield of CO2 from methanogenic biomass yield of hydrogen from primary substrate yield of hydrogen from hydrolytic and/or acidogenic biomass yield of ammonium from hydrolytic and/or acidogcnic biomass experimental yield of a product from a substrate theoretical maximum yield of a product

from a substrate yield of soluble organics from primary substrato yield of soluble organics from hydrolytic

and/or acidogenic bi lmass yield of solid residue from primary substrate yield of solid residue from hydrolytic

and/or acidogenic biomass

yield of methanogenie biomass from H2 yield of methanogenic biomass from acetate yield of hydrolytic and/or acidogenic biomass stoichiometric coefficient characterizing dependence

of the primary substrate hydrolysis rate on the growth rate of hydrolytic and/or acidogenic bacteria

yield of cations other than H + and NH4 + from hydrolytic and/or acidogenic biomass degree of reducibility thermodynamic biological efficiency retention time

- specific growth rate of hydrolytm and/or acidogenio bacteria

kg m -a

kg m-a

kg m-a

kg m -a

kg m -a kg d -1 kg mol-1 kPa kPa mol L - ld -1 m a mol-I m s, L m a, L

kg m-a kg m-a

kg kg -1

kg kg -1 kg kg -1 kg kg -1 kg kg -1

mol kg -1

mol kg -1 kg kg -1 kg kg -1 kg kg -1

mol kg-1 kg kg -1

kg kg kg -1 kg kg -1 kg kg - t

kg kg -1 kg kg -I

kg kg -1 kg kg -1

kg kg -1

kg kg -1 kg kg -1 kg kg-1

kg kg -1

reel kg -1 reel reel-1 1 d

d-1

SS I. HAVLT[K et al. Vat. 31

#AC /~H2 prn

//n'-' kC ItmH2

Iv~dices

AC AC- C CO2 CH4 exp I-I2 HCO3 in M NH3 N H 4

specific growth rate of methanogenic bacteria on a c e t a t e specific growth rate o f methanogenie bacteria on hydrogen maxinmm specific growth rate of hydro ly t i c

and/or aeidogenk ~, bacteria m a x i n m m specific growth rate of ace ta te maximum specific growth rate on hydrogen mass l~atio of carbon

d-1 d-1

d - t d- t d 1 kg kg -t

acetic acid P product acetate anions S substrate carbon sire simulated carbon dioxide SO soluble organ~c.~ methane $1 primary subs~rate experimental $2 solid residue hydrogen un unionizod hydrogen carbonate VA volatile acids inlet VS volatile sohds m e t h a n o g e n i c bacteria, biomass X hydrolytic and/or aeidogenw hiomass a m m o n i a X 3 I methanogenie biomass a m m o n i u m Z c a t i o n s o ther t h a n H + and NHt*

Introduction

Anaerobic digestion is, from the point, of view of microbial process engi- neering, a highly complex process because of the involvement of a number of different microbial species in a mixed population, converting complex substrates of non-standard composition into methane and CO2 gases, solid residue and waste water with a significantly reduced BOD content.

Mixed culture involved in anaerobic digestion consists of four major trophic groups of microorganisms: 1. hydrolytic bacteria that hydrolyze complex organic solids to soluble organic material, neutral compounds and organic acids; 2. hydrogen-produeingacetogcnic bacteria that catabolize certain organic acids to acetic acid and hydrogen; 3. homoacetogenic bacteria, converting H2/CO2 and formic acid to acetic acid; 4. methanogenic bacteria that catabolize acetic acid and one-carbon compounds to methane (Zeikus 19S0).

Dynamic models of anaerobic digestion date from the work of Andrews (1969) and Andrews and Graef (1971), who based their model of municipal waste digestion on Monod inhibition-type kinetics of acetate cleavage to CH4 and C02. Mass balance of the C02--HC03- system in liquid phase together with the balance of C02 between gas and liquid phase are used to model the dynamics of pH of digester content. Hill and Barth (1977) used this concept in the development of a two-culture model of digestion of swine and poultry waste: insoluble organics are converted to CH4 and C02 in two steps, the first being the hydrolysis of insoluble to soluble organics and their s~bsequent conversion to volatile acids represented by acetate. In the second step, acetate is cleaved to CH4 and CO2.

A comprehensive model of anaerobic digestion of animal wastes, where methane is generated both by acetate cleavage and COz reduction by hydro- gen, was recently published by Hill (1982). In this model, all hydrogen produced is assumed to be utilized in the subsequent metabolic stage to form either methane or acetate, and no hydrogen appears in the digester off-gas. Small amounts of hydrogen, of the order of 100 ppm, are, however,

1986 ANAEROBIC DIGESTION" PROCESS $$

found in the gas phase of digesters (Fischer et al. 1983). The role of hydrogen seems to be decisive in the regulation of consecutive metabolic reactions carried out by different microbial groups, and the hydrogen content in the digester gas phase can be a fast and reliable means of early detection of digester failure (Wolin and Miller 1982). Modelling of hydrogen metabolism and liquid--gas phase balance seems thus to be necessary in a successful digestion model.

As the first step towards a description of complete microbial system of anaerobic digestion, a two-step model is proposed. In the first step, primary solid substratc is solubilized and converted to acetate, hydrogen, carbon dioxide and solid residue. In the second step, acetate and H2/COu are meta- bolized to methane.

The stoichiometry of hydrogen production from pure substrates (e.g. glucose, butyrate, propionate) can be reliably assessed experimentally. With complex substrates, distribution of energy flow in the first digestion stage between hydrogen and acetate can be obtained by means of mass a n d energy balance of carbon and available electrons (redoxons). This method was, in general form, described by Reels (1980) and Erickson et al. (1978) and further extended and applied to anaerobic digestion processes bySob~atka et al. (1983).

Mass and energy balance

The degree of reducibility of a given organic compound (~) of a general ~ormula CHaObNz and mass content of carbon (a) in this compound are denoted as

y = + a - 2 b - - 3z (1)

a : M c / M (2)

where Mc is the molar mass of carbon and M the molar mas~ of 1 ~C-mol of the compound. (a C-mol is an amount containing I tool of carbon), Maximum theoretical yield of conversion of substrate S to product P is then given by

Y~ /~ = asrs/ ae~,P (3)

Knowing the experimental values of product yield YEp/s we can define the thermodynamic biological eefficiency of the process

WE I'~TT = Pl~lXp/s (4)

Overall stoichiometry of the anaerobic digeStion process can be described by means of energy flow, represented by redoxons, and flow of carbon (Fig. l).

For the purposes of overall stoiehiometry the following stoichiomet~o coefficients have to be assessed: yield of methane from primary substrate 81 (](CH4S1) and yield of digested s~lid residue Sz (YS2SI). The stoichio. met ry of intermediates is represented by the yield of H~ from $1 (u a n d the yield of acetate from $1 (u The stoichiometry of the terminal stages, i.e. methanogenesis from acetate, is experimentally known, as well

s the stoiehiometry of methanogenesis from hydrogen. a The overall balance of available electrons (Fig. 1 right) in a methanogenie process can be written as (note: 7/co2 ~ 0)i

~nslaslTsx/12 ~ Ths2asJys~/12 -~ ?~CH40"CH4~CH/]~ (5)

60 I. ]-IAVL:[K et al. Vol. 31

d

2

Primary substrate

$1

Solubi l ized primary substrata

SO

= Primer)' substrate

So[ubi l ized primary substrata ]

I

FIG. 1. Carbon (left) and re(loxon (right) flow in the anaerobic digestion proce.~s.

where m s l , ms2 and ~hc~4 denote mass flow of pr imary substrata, solid residue (including biomass) and produced methane, respectively. After rearrange- ment, the yield of solid residue is given by

YS2S1 ----- (aslTsl -- 6cit47cH4 YCH4S1)/assTs2 (6)

The overall balance of carbon (Fig. 1 left) is:

" O'SlmSl = o'ssmss -~- 0"CH4mCH4 -~- ffco2mco2 (7)

which results in

u ---- aSl(1 -- acH4YCH4S1/aSl -- assYS2S1/aSl)/acoz (8)

Mass balance in the first metabolic stage, where hydrogen and acetate are produced as intermediates, can be derived as follows: let us assume an " ideal" stoiehiometry of methanogenesis from Hz/COs and acetate:

4 Hs -J- COs = CH4 + 2 H20; CH20 = 0.5 CH4 -k 0.5 C09. (9)

and the overall conversion scheme:

a' tool CHs0 a tool CHa Sz § b ' m o l C 0 s - - § b m o l C 0 s (10)

d' mol H2 c mol $2 c mol $2

where, according to (9): a = a'/2 + d'/4 (11)

Let us denote the ratio of hydrogen produced in the first digestion stage to acetate produced there as u When (11) and the equation

u ---- YH2S 1/YACS 1 (12)

are combined, the following yield coefficients are obtained:

u =- 4 YH2AC YCH4S1 MAcMH2/Mc~4 (2 M~s ~ YH2AC MAc) (13 i

YACS1 = 4 YCH4S1 MAcMHs/McHa(2 M~s ~ YH2AC MAc) (1.4)

1986 ANAEROBIC DIGESTION PROCESS 61

where MAC, M~e and MCH4 are the molar masses of acetate (1 C-mol), hydro- gen and methane, respectively. Equat ions (13) and (14) enable us to describe the distribution of intermediates produced from pr imary substrate on the basis of known ultimate methane yield from pr imary substrate (YCH4S1) and the known ratio of CHa formed via H2/C02 pa thway to the CH4 formed via acetate pathway. Under s teady-state conditions, the portion of energy transferred via hydrogen is approx. 30 ~ of the total energy transfer from substrate to methane (Smith and Mah 1966). The turnover of acetate and hydrogen can be thus modelled on the basis of strict mass and energy balance.

Model description

The two-culture mathematical model of continuous animal waste digestion as presented by Hill and Barth (1977) was extended with the description of methanogenesis via the He/COs pa thway and gas-- l iquid phase balance of hydrogen.

The primary substrate hydrolysis is described as

~sl = D(eslin -- Csl) -- juX/YXSO (15)

Cso : D(csoin -- cso) -- [ ~ X / Y X S --~ ~ X YSOX (16)

Cse ~ -- Dcs2 ~ I~X YS2X (17)

where D is the dilution rate, # is the growth rate of hydrolytic and/or acido- genie bacteria, X their biomass concentration, Cso the concentration of solubilized pr imary substrate (the chemical formula of glucose is assumed).

The balance of acetic acid, produced from solubilized pr imary substrate, is given by

CAC = D(ChCin - - CAC) -~ ~aX u -- #AcXM/YXSM (18)

Here /~Ac is the growth rate of methanogenic bacteria on acetate and XM their biomass concentration.

The biomass of hydrolyt ic and/or acidogenic bacteria X and biomass of methanogenic bacteria XM is balanced as

J~ ---- D(Xin - - X ) ~- ~ X - - K D X (19)

J~M = D(XMin - - XM) "~- [~MXM -- KDMXM (20)

where KD and KD~I are death rate coefficients. There are three gaseous substances to be balanced between the liquid and

the gas phase: COs, H2 and NHa. Carbon dioxide and ammonia are also par t of the digester buffering system, in the ionic form of HCO[ and ~ H ~ , together with organic acids. Methane is considered as insoluble in the liquid phase, because its phase balance is of no consequence to either microbial kinetics or buffering properties of the digester contents.

Mass balance of dissolved C02 is described by

r xM ~co2 ---- D(cco2i, -- Cco~. -t- C~co3in -- CHCO3) + r~o~ -{- r ~- ..}_ x cos rco2 r~c2 + ~ c _ r z _ N . 3 _ r ~ o 2 (21)

where r~o~ = IcLa(KHco2Pco2 ~ Cco2) (22)

62 I. HAVL~K et al. Vol. 31

is t h e rate of C02 transfer to the gas phase, o x rco~ = #~XM YCO2XM (23)

is the rate of C02 production due to cleavage of acetate,

r~o~ = reX Y C O 2 X / M c o 2 (24)

is the rate of C02 production in the hydrolytic and/or aeidogenic stage,

rco2re _~ dAc/MAe (25)

is the rate of COz release from HCO~ due to the production of acetic acid in the acidogenic stage,

(s *,he rate of CO2 consumption in the HCO~-forming reaction due to cation other than Ntt~ and H+) release from primer y substrate,

rco~~'a = CNH4/MNH4 ('27)

is the rate of CO2 consumption in the HCO~-forming reaction due to release of NH~ from primary substrate,

rco2 )~ = /~H2X.~/(4. YXMH2 MH~) (28)

is the rate of CO2 consumption by methanogenie bacteria. Balance of dissolved He is calculated as (He concentration in the influent

is assumed to be zero):

cn2 = --DCH2 + f i x YH2X -- #tt2X.~I/YXMH2 -L- k L a ( K I ~ 2 P H 2 - - CH.)) (29)

Mass balance of ammonium is calculated by

+ k L a ( K H ~ H a P ~ I 3 - - c . ~ a ) M ~ i a (30)

Concentration of ammonia in the liquid phase, necessary for equations (33), (42) and (43), is calculated as

CNH3 ~-- C.NK4KNH4/CH'~MNH4 (31)

Partial pressures of CO2, NH3, He and CH4 in the digester g~as space a~':; calculated from mass balances on the assumption of constant total pr~,s~re in the digester:

P i = P r F i / V g - - P i F / V g (32) where

F i = - - S V k L a V ( K H ~ P ~ - - ci) , / = C02, NHa, H2 (33) and

-FCH4 = luAcXM YCH4X V BV -?/~zX.~ YCH4XH V SV (34)

F ---- Fco2 § F~Ha + F~2 + Fc~4 (35)

Balance of inorganic cations other than NH4 + and H +, released from the pr imary sludge by hydrolysis, is given by

Cz --~ D(Czin =- vZl -}-/tX Y Z X (36)

198g A N A E R O B I C D I G E S T I O N PROCESS 63

T~lgL]g I. Values of cons tan ts and independent pa ramete r s used in the model

Constant Value Dimension Reference

K s 0.150 kg SO m -a Hill and Bar th (1977) K i 1.0 kg ACun m-3 dit to pm " 0.4 d -1 dit to KD 0.025 d -1 di t to KAC adjus ted kg ACun m-3 -- KiAc 0.3 kg ACun n1-3 Hill and Bar th (1977) KiNn3 1.8 kg NH3 m -s Hill and Nords ted t (1980) /tmAc 0.4 d -1 Hill and Bar th (1977) KHs 17.2 x 10 -6 kg H2 m -3 Scott et al. (1983) pmr~2 1.4 d -1 Weimer and Zeikus (1978) KDM 0.04 d -1 Hill and Bar th (1977) "Y'CH4AC~ 0.259 kg CH4 kg-1 AC Zinder and Mah (1979) YCH4H2 2.15 kg CH4 kg-1 H2 Rober ton and Wolfe (1970) YCH4S1 adjus ted kg CH4 kg -1 $1 -- YH2AC 0.056 kg H2 kg -1 AC computed Y X S O adjusted kg X kg -1 SO -- Y X S adjusted kg X kg -1 SO -- Y X M H 2 0.93 kg X ~ kg-1 H2 Rober ton and Wolfe (1970)

Weimer and Zeikus (1978) YXSM 0.06 kg X ~ kg -1 AC . Hill and Bar th (1977) YNI~4X 0.1212 kg NH4 + kg -1 X dit to Y Z X 4.8 • 10 -6 mol Z+ kg-1 X Hill and Nords ted t (1980) kLa 10 d -1 Hitt and Bar th (1977) K]FlCO2 2.6 X 10-4/35 ~ tool kPa -1 L -1 Weast (1967) KnH2. 7.4 ~,: 10-6/35 ~ tool kPa 1 L-1 Perry (1950) K14~:n3 4.0 x 10-5/35 ~ tool kPa -1 L -1 Hill and Bar th (1977) KNH4 5.3 • 10-10/35 ~ 1 Weast (1967) /~co2 4.7 x 10-7/35 ~C 1 di t to M x . 0.113 1.:g tool 1 Hill ~md Bar th (1977) Mx,~ 0.113 kg lno1-1 dit to PT 97.3 kPa -- S V r ~ m a tool -1 Hill and Bar th (1977) as1 0.4475 (pig) kg C kg -1 Sobotka et el. (1983)

40.4213 (beef) dit to ysl 3,931 (pig) tool AE/mol C dit to

3.934 (beef) d i t to as2 0.4 kg C kg 1 Hash imoto et al. (1981) 7s2 2.7 mol AE/mol C dit to

Calculation of pH of digester content is csrried out on the basis of the charge balance between cations and anions and mass balance between ionized and unionized acetic acid:

CHC03 ~-- CZ § C~'H4 - - CAC-

CAC- = CAC - - CACun

CH + = (Kco2Cco2) /CHC03

(37)

(3s)

(39)

l i inetics of microbial (trowth

Growth function p of hydrolytic and/or acidogenic bacteria includes inhibition by unionized acetic acid:

u = ~, .cso/( / ;s § Cso § cAc~dSo/K,) (40)

64 I. H A V L f K et al. Vol. 31

TABLE I I . Influent and effluent data of a s teady-s ta te cont inuous digestion process. Digestion t empera tu re lay in all cases in the mesophilic range (35--38 ~

Inf luent characteristics and composit ion

D a t a Waste eva Cvs ]Reference No. type kg m -3 kg m - a

1 pig 4.6 60.3 Fischer et al. (1979) 2 pig 4.0 56.9 Iano t t i et al. (1979) 3 pig 5.3 29. l van Velsen (1981) 4 pig 5.3 29.1 dit to 5 pig 8.0 43.6 dit to 6 pig 8.0 43,6 ditto 7 beef 9.5 70.0 Gosh et ul. (1981) 8 beef 10.0 71.0 dit.to 9 beef 10.3 81.5 ditto

10 beef 10.0 71.4 dit to

Exper imen t characteristics and effluent composi t ion

D a t a V O FcH4 a CvA Cvs p H No. L d L d - I kg m-8 kg m z 1

1 420 b 15 573 0.370 23.9 7.6 2 420 b 15 566 0.800 23.2 7.6 3 1.5 c ]5 0.828 0.774 19.8 7.6 4 1.5 e 10 0.886 2.316 21.7 7.45 5 6 e 20 3.97 0.186 33.9 7.7 6 5 e 20 3.06 0.330 29.7 7.8 7 51 000 d 12 50 000 2.3 50.0 7.5 8 9 e 10 10.5 2.2 55.8 7.5 9 9 c 17 7.9 2.4 55.1 7.7

l0 9 c 25 5.79 1.4 49.8 7.6

a Exper imen ta l methane produc t ion K, 101.325 kPa).

b Pilot-size experiment. c Laboratory-size experiment . a Full-scale digester.

rate, FcH4, is given as L d -1 at s tandard condit ions (273.15

where Ks is the saturation constant and Ki the inhibition constant of union- ized acetic acid. A homogeneous methanogenic bacterial population utilizing simultaneously both acetate and hydrogen is considered. The growth flmction #u of methanogenic bacteria is given by

~/~ ~-~ ~AC -~- ~H2 (41)

/tAC = ttmACCACun/(KAc -~- CACun @ r ~[- CNH3CACun/KiNtt3) (42 )

~UtI2 = ttmtt2CH2/(gH2 ~- CH2 ~- CACunCH2/KtAc -~ CNtt3CH2/KiNH3 (43)

where/~m are the maximum specific growth rates, KH2 and KAc the saturation constants, KiAc and Ki~Ha the inhibition constants of unionized acetic acid and ammonia, respectively.

198~ A N A E R O B I C D I G E S T I O N PROCESS 65

TABLE I I I . Simulated da ta of s teady-state cont inuous digestion process

Da ta PH2 FC]ff4 a eVA CV$ p H No. Pa L d -1 kg m -3 kg m-3 1

1 8.3 548 0.403 ~ 23.3 2 1.9 556 0.660 22.0 3 4.4 0.707 0.795 19.8 4 5.3 0.857 2.310 21.2 5 3.2 2.87 0.182 33.2 6 2.8 2.84 0.378 28.9 7 4.5 39 200 2.39 48.8 8 5.3 7.11 2.20 55.7 9 3.9 5.6 2.40 55.1 �9

10 4.6 3.52 1.68 49.7 .

7.6 7.5 7.3 7.3 %6 7.7 7.6 7;5 7.9 7 . 6

Deviat ion of s imulated and exper imental da ta b

Maximum deviat ion 39.2 19.3 2.7 Minimum deviat ion 3.2 0 0 Average deviat ion 18.7 7.2 1.4

3.9 0 1.9

a Simulated methane product ion rate, Fc~4, is given as L "d ~1 at s t andard c o n d i t i o n s (273.15 K, 101.325 kPa).

b Defined as: & = 100 lYo~p - Y~I/Y~p (%)

Average deviation, Aav = ( Z Al)/10 i = l , 10

Evaluation of stoichiometric coefficients and constraints

For hydrogen a n d acetate production from primary substrate, equations (13) and (14) are used. For the YH2AC value, formation of 0.485 mol CHa per ] C-mol of acetate (Zinder and Mah 1979) and 0.265 mol CH4 per l mol of hydrogen (Roberton and Wolfe 1970) is assumed. Values of as~ and ys~ (as2 = 0.4, ys2 ~ 2.7), necessary for balances (6)'and (8), have been computed from data of Hashimoto et al. (1981i~ values of~asl and ~s~ of pig and beef manure are taken from Sobotka et al, (1983).

Values of physico-chemical constants, kinetic~ constants and independent yield coefficients are given ifi Table/:- 'Kinetic affd stoichiometric parameters used in model, tha t were taken from literature, were obtained from exper- iments with pure cultures of methanogenic bacteria (#m~, YCH4AC, YCH4H2, YH2AC, YXMH2), from experiments with mixed cultures on complex substrates ~ (K~2, ~gi, 7si, ass, ys~), or, Were, estimated, 'by ~mela~si b~f computer simulation 'Of digestion 'of complex substrates (:Ka~ Ki~, * Km:K'i~c, KiNH3, ~m, tZmAC, KDM, ;YNI-i4X, ~YZX): ' ' " ,

.Values 'of dei)endent: yieId, coeff icients a re derive@from ~r ba~io ~ser of infleper/dent ~oefficients (YXSO, YXS,Y)~SM, u Y~Mtt2~ u YCH4S'I) arid f t0m coefficients obtained in (6). -- (14,) ~s, follows :'

YSQS1 =',YACS ! qxc/aso, Y s O X , = YS,OSl/:YXS0

~$ I . H A V L ~ K e t a L " V o l . 3 1

YCH4X = YCO2XM = YCO2T = YCO2X ~-- YACX = Y C H 4 X H Y H 2 X =

YCH4AC/(YXSM Mc~4) YCH4X (aSl =- as2 YS2S1 -- aso YSOS1)/aco2 YCO2T/YXS0 Y A C S 0 / Y X S YCH4H2/ (YXMH2 Mc~4) YH2S1/(YSOSI. YXS)

(4~)

Result s of model identification

Literature data from continuous digestion of swine and beef waste, namely methane production rate FcHa, concentration of volatile acids (as acetate) in effluent, volatile sol ids concentration in effluent (Cvs = Csl + Cs2) and p H in the digester were used for model validation. Testing of parametric sensitivity of these model outputs to individual model parameters (Havllk et al. 1984) let to the choice of adjusted model parameters: YXSO, YXS, KAc and YCH4S1. Identification of the model has been carried out for steady- state values of process variables, using nonlinear regression. Experimental da ta used for identification, together with specification of conditions under which they were obtained (i.e. experiment size, waste type, retention time, methane production rate, p H of digester content, volatile solids and volatile acids content both in the digester and in the influent waste) are given in Table II. Temperature in all cases is in the mcsophilic range (35--38 ~

TABLE IV. P a r a m e t e r va lues of the ident i f ied mode l

D a t a Y X S O Y X S KAc YCH4S 1 No. X 10 a X 10 a x 10 -3 x 10 a

1 734 687 0.98 289 2 460 545 2.8 281 3 513 530 4.8 285 4 783 801 9.3 286 5 596 592 0.72 285 6 715 766 1.1 288 7 505 537 7.8 273 8 529 547 7.2 266 9 770 860 5.9 270

10 487 516 9.8 275

All experimental da ta used here are reported to have been obtained under s teady-state conditions of a mixed, continuous digestion process. Results of model identification are summarized in Tables I I I and IV.

Comparison of experimental data with simulated model outputs shows a close agreement in Cvs, eva (acetate) and p H in effluent. The hydrogen content in the gas phase corresponds well to the various experimental data described in the literature (1--30 Pa; Fernandes X., Mosey F. E.: _Personal communication; Fischer et al. 1983). The simulated methane flow rate is systematically lower than the experimental value (Fsim = (61--97 ~ ). with an average value of Fsim ~-- 0.8 Fexp. As methane yield from

i986 ANAEROBIC D][GESTION P R o c E s s 6?

primary substrate~(YCH4S1) is restricted from above by redoxon ba- lance (6), these discrepancies result probably from the fact that influent volatile acids in the model arc considered to consist only from acetate. Other organic acids (mostly energy-richer propionic and butyric acid), forming a substantial part of total influent volatile acids, are not taken into account. As the theoretical methane yield from these acids, computed from (3), is higher than that of acetate (0.267, 0.378 and 0.455 g CH4 per g acid for acetic, propionic and butyric acid, respectively), inclusion of the propionic and butyric acid balance into the modelled process variables will lead to a closer agreement between simulated and experimental data and seems to be necessary from the point of view of the strict carbon and energy balance.

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